Existence of a Steady Flow of Stokes Fluid Past a Linear Elastic Structure Using Fictitious Domain

We use fictitious domain method with penalization for the Stokes equation in order to obtain approximate solutions in a fixed larger domain including the domain occupied by the structure. The coefficients of the fluid problem, excepting the penalizing term, are independent of the deformation of the structure. It is easy to check the inf-sup condition and the coercivity of the Stokes problem in the fixed domain. Subtracting the structure equations from the fictitious fluid equations in the structure domain, we obtain a weak formulation in a fixed domain, where the continuity of the stress at the interface does not appear explicitly. Existence of a solution is proved when the structure displacement is generated by a finite number of modes.     

Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides

We consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in the unbounded straight parts of the guide. Each algorithm can be related to a so-called domain decomposition method, with an overlap between the domains. Specific transmission conditions are used, so that at each step of the algorithm only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using a bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized. An original choice of transmission conditions is proposed which enhances the effect of the overlap and allows us to handle arbitrary anisotropic materials. As a by-product, we derive transparent boundary conditions for an arbitrary anisotropic waveguide. The transparency of these new boundary conditions is checked for two- and three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for two- and three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time.     

An approach for analytical solution pertinent to lattice temperature variation due to laser short-pulse heating

Non-equilibrium energy transport in the surface region of the metallic substrate occurs due to a laser irradiation, which in turn results in thermal separation of electron and lattice sub-systems. As the heating period exceeds the thermal relaxation time, both sub-systems become thermally in equilibrium having the identical temperatures. When electron and lattice temperatures become identical the corresponding instant can be called thermal equilibrium time. In the present study, an analytical formulation of lattice site temperature distribution in the domain of thermal equilibrium time is obtained. Temperature differences and temperature distributions in electron and lattice sub-systems are computed for gold. It is found that electron and lattice temperatures become identical for the heating period beyond the thermal equilibrium time. Temperature distribution obtained from the analytical solution and numerical predictions agree well.     

Multiscale modeling of the dynamics of solids at finite temperature

We develop a general multiscale method for coupling atomistic and continuum simulations using the framework of the heterogeneous multiscale method (HMM). Both the atomistic and the continuum models are formulated in the form of conservation laws of mass, momentum and energy. A macroscale solver, here the finite volume scheme, is used everywhere on a macrogrid; whenever necessary the macroscale fluxes are computed using the microscale model, which is in turn constrained by the local macrostate of the system, e.g. the deformation gradient tensor, the mean velocity and the local temperature. We discuss how these constraints can be imposed in the form of boundary conditions. When isolated defects are present, we develop an additional strategy for defect tracking. This method naturally decouples the atomistic time scales from the continuum time scale. Applications to shock propagation, thermal expansion, phase boundary and twin boundary dynamics are presented.     

Two‐level finite element method with a stabilizing subgrid for the incompressible MHD equations

We consider the Galerkin finite element method (FEM) for the incompressible magnetohydrodynamic (MHD) equations in two dimension. The domain is discretized into a set of regular triangular elements and the finite‐dimensional spaces employed consist of piecewise continuous linear interpolants enriched with the residual‐free bubble functions. To find the bubble part of the solution, a two‐level FEM with a stabilizing subgrid of a single node is described and its application to the MHD equations is displayed. Numerical approximations employing the proposed algorithm are presented for three benchmark problems including the MHD cavity flow and the MHD flow over a step. The results show that the proper choice of the subgrid node is crucial to get stable and accurate numerical approximations consistent with the physical configuration of the problem at a cheap computational cost. Furthermore, the approximate solutions obtained show the well‐known characteristics of the MHD flow. Copyright © 2009 John Wiley & Sons, Ltd.     

On the relative stability of the crystal structures of iron

Iron has ab.c.c, structure below 1183GK and above 1670GK In between it has anf.e.c, structure. In this paper the free enthalpy of ab.e.c, lattice and af.c.c lattice is calculated from an interatomic potential of the Morse type. The parameters of the Morse potential are considered as functions of temperature and their values are determined from macroscopic measurements of the lattice constant, the enthalpy and the entropy. The calculated free enthalpies exhibit intersections that correspond to the observed phase transitions. The intersections occur at temperatures which are close to the observed transition temperatures.     

Energy release rate approximation for small surface-breaking cracks using the topological derivative

The topological derivative provides the variation of a response functional when an infinitesimal hole of a particular shape is introduced at a point of the domain. In this fracture mechanics work we use the topological derivative to approximate the energy release rate field associated with a small crack at any boundary location and at any orientation. Our proposed method offers significant computational advantages over current finite element based methods since it requires a single analysis, whereas the others require a distinct analysis for each crack location-orientation combination. Moreover, the proposed method evaluates the topological derivative in the non-cracked domain which eliminates the need for tailored meshes in the crack region.     

Metastability and Dynamics of Discrete Topological Singularities in Two Dimensions: A Γ-Convergence Approach

This paper aims at building a variational approach to the dynamics of discrete topological singularities in two dimensions, based on Γ-convergence. We consider discrete systems, described by scalar functions defined on a square lattice and governed by periodic interaction potentials. Our main motivation comes from XY spin systems, described by the phase parameter, and screw dislocations, described by the displacement function. For these systems, we introduce a discrete notion of vorticity. As the lattice spacing tends to zero we derive the first order Γ-limit of the free energy which is referred to as renormalized energy and describes the interaction of vortices. As a byproduct of this analysis, we show that such systems exhibit increasingly many metastable configurations of singularities. Therefore, we propose a variational approach to the depinning and dynamics of discrete vortices, based on minimizing movements. We show that, letting first the lattice spacing and then the time step of the minimizing movements tend to zero, the vortices move according with the gradient flow of the renormalized energy, as in the continuous Ginzburg–Landau framework.     

The bending,stability and vibrations of rectangular plates with free edges on elastic foundations

This paper discusses the problems of the bending, stability and vibrations of the rectangular plates with free boundaries on elastic foundations. In the present paper we select a flexural function, which satisfies not only all the boundary conditions of free edges but also the conditions at free corner points, and consequently we obtain a better approximate solution. The energy method is used in this paper.     

Variational asymptotic homogenization of temperature-dependent heterogeneous materials under finite temperature changes

The variational asymptotic method is used to construct a thermomechanical model for homogenizing heterogeneous materials made of temperature-dependent constituents subject to finite temperature changes with the restriction that the strain is small. First, we presented the derivation for a Helmholtz free energy suitable for finite temperature changes using basic thermodynamics concepts. Then we used this energy to construct a thermomechanical micromechanics model, extending our previous work which was restricted to small temperature changes. The new model is implemented in the computer code VAMUCH using the finite element method for the purpose of handling real heterogeneous materials with arbitrary periodic microstructures. A few examples including binary composites, fiber reinforced composites, and particle reinforced composites are used to demonstrate the application of this model and the errors introduced by assuming small temperature changes when they are not necessarily small.     

Molecular Dynamics Simulation on Hydrogen Ion Implantation Process in Smart-Cut Technology

The hydrogen ion implantation process in Smart-Cut technology is investigated in the present paper using molecular dynamics(MD) simulations.This work focuses on the effects of the implantation energy,dose of hydrogen ions and implantation temperature on the distribution of hydrogen ions and defect rate induced by ion implantation.Numerical analysis shows that implanted hydrogen ions follow an approximate Gaussian distribution which mainly depends on the implantation energy and is independent of the hydrogen ion dose and implantation temperature.By introducing a new parameter of defect rate,the influence of the processing parameters on defect rate is also quantitatively examined.     

局域共振型声子晶体板缺陷态带隙及其俘能特性研究

设计了一种由圆柱形散射体嵌入环氧树脂基体而组成的周期阵列局域共振型声子晶体板结构,分析了其平直带区域以及缺陷态的能量集中特性,并研究了其振动能量采集特性.首先基于超元胞法结合有限元方法分析了5×5完美声子晶体结构和缺陷态声子晶体结构的能带曲线和能量传输特性;考虑点缺陷局域共振声子晶体结构的能量集中特性,利用压电材料代替...     

Approximation and Calibration of Nonlinear Structural Dynamics

In this paper, a methodology for the calibration of nonlinear structural dynamic models is presented. Calibration of nonlinear structural dynamics offers several additional challenges beyond that of linear dynamics. Even with advanced computational power, exact nonlinear finite element simulations often take several hours to complete on engineering workstations. Thus, the proposed model calibration method utilizes an approximate structural model. This approximate analysis is embedded in the outer loop, which utilizes an exact finite element analysis to verify the validity of the approximate model. If the approximate model is shown to be invalid at that point in parameter space, then the new exact analysis is used to develop an improved approximate model and the inner loop is executed again. Specifically, this paper will focus on the two key aspects of the inner loop, namely the development of an approximate model, and the parameter identification using the approximate model.     

激光加热金属薄膜的热弹性研究

基于电子-声子相互作用的双曲两步热传导模型的超快热弹性理论,计及晶格的热传导效应,利用有限元方法研究了无限大金属薄膜在短暂激光冲击下诱导的位移、应力、应变和温度等物理量的演化特点,与已有文献比较,说明该方法的合理性与正确性.比较了计及电子热爆发力与不计电子热爆发力对位移、应力等物理量的影响,说明计及电子热爆发力的必要性...     

Measuring the efficiency of vertical drill-strings: A vibration perspective

A drill-string is a slender structure with nonlinear dynamics; it is an equipment used in the oil industry to drill the rock in the search of oil and gas. The aim of this paper is to investigate the efficiency of the drilling process in terms of input/output power. The continuum system is linearized about a prestressed configuration, the finite element method is applied to discretize the linear system, then a reduced-order model is constructed using the normal modes of the linear system; only torsional and axial vibrations are considered in the analysis. Uncertainties related to the speed imposed at the top are also included in the analysis. The rotational top speed is modeled using two different stochastic processes and the Monte Carlo Method is employed to approximate the statistics of the response of the resulting stochastic differential equations.     

Thermodynamic restrictions,free energies and Saint-Venants principle in the linear theory of viscoelastic materials with voids

This paper examines the thermodynamic restrictions imposed by the second law of thermodynamics upon the relaxation functions in the linear theory of viscoelastic materials with voids. On this basis the existence of a maximal free energy is proved by means of a constructive method. Further, we use such a maximal free energy in order to establish a principle of Saint-Venant type in the dynamics of viscoelastic materials with voids. A uniqueness theorem is proved for finite and infinite bodies and we note that it is free of any kind of a priori assumptions concerning the orders of growth of solutions at infinity.     

An Experimental Facility to Measure the Chemorheological Response of Inflated Elastomeric Membranes at High Temperature

An experimental facility for measuring the time-dependent deformation of an inflated elastomer membrane at elevated temperatures is presented. The facility controls the temperature and inflation volume of a membrane specimen and measures the pressure and deformation field. The finite deformation field is determined by comparing the configuration of the inflated membrane to the initially flat reference configuration, determined by photogrammetry of an array of dots printed on the surface of the membrane. The facility provides an effective method to investigate the changes in mechanical properties due to scission and cross-linking in the context of a simple elastomeric structure that has a distribution of multi-axial deformation states.     

Extension of domain‐free discretization method to simulate compressible flows over fixed and moving bodies

This paper is the first endeavour to present the local domain‐free discretization (DFD) method for the solution of compressible Navier–Stokes/Euler equations in conservative form. The discretization strategy of DFD is that for any complex geometry, there is no need to introduce coordinate transformation and the discrete form of governing equations at an interior point may involve some points outside the solution domain. The functional values at the exterior dependent points are updated at each time step to impose the wall boundary condition by the approximate form of solution near the boundary. Some points inside the solution domain are constructed for the approximate form of solution, and the flow variables at constructed points are evaluated by the linear interpolation on triangles. The numerical schemes used in DFD are the finite element Galerkin method for spatial discretization and the dual‐time scheme for temporal discretization. Some numerical results of compressible flows over fixed and moving bodies are presented to validate the local DFD method. Copyright © 2006 John Wiley & Sons, Ltd.